An unexpected run on parts at a maintenance supervisor's desk apparently led to the loss of all three engines and the dramatic emergency landing in Miami Thursday of an Eastern Airlines jumbo jet carrying 172 people, federal investigators said yesterday.

That was what National Transportation Safety Board officials discovered after interviews with one of the mechanics and others responsible for servicing the Lockheed L1011 in Miami Wednesday night. Critical oil seals were not reinstalled in the three jet engines, and all three failed on a Miami-to-Nassau flight before the crew was able to restart one engine and make a safe emergency landing back in Miami.

The seals surround a bolt that is driven into the oil line in the engine. The bolt, 2 inches long and 5/8-inch in diameter, is magnetized to capture tiny metal chips that might appear in the engine oil. The bolt is withdrawn daily and inspected to see if it has collected any chips, which would be a sign of engine problems.

After the interviews yesterday, safety board spokesman Ira J. Furman said, investigators put together this sequence of events:

The usual procedure is for one mechanic to remove the bolt and oil seals from the two wing engines and for another mechanic to remove the bolt and seals from the tail engine. A valve keeps the oil from spilling while the bolts are changed.

The dirty bolts and seals are placed in plastic containers and delivered to a supervisor. The supervisor gives the mechanics different containers with inspected and cleaned bolts and oil seals. The mechanics reinstall the bolts and seals.

Wednesday night, however, when the Nassau-bound plane and other L1011s were undergoing routine checks, the supervisor ran out of replacement bolts and seals. A mechanic, either at a supervisor's direction or on his own, went to a supply area to get more bolts.

He found containers that look like the containers his supervisor usually would give him and passed them out. Those containers held bolts but no oil seals, because the seals are stored separately and joined with the bolts at the supervisor's desk. The absence of seals was not noticed, however, and the bolts were installed.

Oil will not leak until the engine's turbine is set in motion. It is normal procedure to do that as a test, without starting the engine. Furman said the plane's engines apparently were tested, but it is not known for how long. Safety board officials found that it takes at least 20 seconds of testing to cause an engine oil leak.

The two mechanics and the supervisor involved were not identified. The mechanics were both at least 10-year Eastern veterans, Furman said. Eastern officials would not say what, if any, disciplinary action is anticipated.

Federal sources said there is nothing in the investigation so far that would indicate that the missing seals constitute anything more than a potentially tragic inadvertance.